1. Estimation of Tidal Current using Kalman Filter Finite Element Method with AIC Ryosuke SUGA Chuo university D EPARTMENT OF C IVIL E NGINEERING F ACULTY OF S CIENCE AND E NGINEERING Second MIT Conference on Computational Fluid and Solid Mechanics

2. Introduction In a seaside area, various structures are built in Japan. To grasp the state of the sea around a seaside area JAPAN The mechanical and the manual error are included in the observation data. (observation noise) A numerical model cannot express the physical phenomena completely. (system noise) It is difficult to set many observation points economically. Important Kalman filter finite element method Second MIT Conference on Computational Fluid and Solid Mechanics

3. Kalman Filter To be presented by Kalman and Bucy in 1960’s the filtering algorithm based on stochastic process including noises Since the noise is taken into consideration, Kalman filter can remove the noise. It can estimate the state estimative value only in time series. aerospace science, control engineering and civil engineering Kalman filter Observation data Estimation value (+ noise ) Second MIT Conference on Computational Fluid and Solid Mechanics

4. Kalman Filter Finite Element Method The conventional Kalman filter can not estimate the state values in space model. Kalman filter + finite element method It is possible to estimate the state estimative values not only in time series but also in space model. This method is possible even if it is a large-scale domain. Second MIT Conference on Computational Fluid and Solid Mechanics

5. Purpose To present Kalman filter finite element method To estimate of tidal current using Kalman filter finite element method Second MIT Conference on Computational Fluid and Solid Mechanics

6. The state-space model of the Kalman filter : State vector at time k: State transition matrix : Driving matrix: System noise : Observation vector: Observation matrix : Observation noise Kalman Filter Second MIT Conference on Computational Fluid and Solid Mechanics Applying the finite element equation

7. Second MIT Conference on Computational Fluid and Solid Mechanics 1. if goto 6 then else goto 2 2. 3. 4. 5. Off-line 6. 7. On-line Algorithm

8. Shallow water equation h : Water velocity: Gravitational acceleration : Water elevation : Water depth Second MIT Conference on Computational Fluid and Solid Mechanics Basic Equation

9. Finite Element Method The spatial discretization The temporal discretization Galerkin method BTD method Finite element equation Second MIT Conference on Computational Fluid and Solid Mechanics

10. Kalman Filter + Finite Element Method Finite element equation State transition matrix State vector Finite element matrix Second MIT Conference on Computational Fluid and Solid Mechanics

11. 1. if goto 6 then else goto 2 2. 3. 4. 5. Off-line 6. 7. On-line Second MIT Conference on Computational Fluid and Solid Mechanics Algorithm

12. Akaike Information Criterion (AIC) AIC is the criterion of the selected one from the models which applied maximum log-likelihood method. Maximum log-likelihood method is the way to choose the value of mother group that has the possibility to produce observed sample larger than something else.

13. Numerical Example Estimation of tidal current using KF-FEM Onjuku coast The water pollution moves ahead with the inflow of pollution material. Second MIT Conference on Computational Fluid and Solid Mechanics

14. Numerical Model Onjuku coast Onjuku Coast Iwawada Port No.5 No.4 No.3 No.2 No.1 Onjuku Port Second MIT Conference on Computational Fluid and Solid Mechanics

15. Node : 407 Element : 728 (m) Finite Element Mesh and Water Depth Second MIT Conference on Computational Fluid and Solid Mechanics

16. Observation Data at NO.1 Onjuku Coast Iwawada Port No.5 No.4 No.3 No.2 No.1 Onjuku Port ObservationEstimation

17. Onjuku Coast Iwawada Port No.5 No.4 No.3 No.2 No.1 Onjuku Port ObservationEstimationResult

18. Second MIT Conference on Computational Fluid and Solid Mechanics Result

19. Conclusion The tidal current was estimated using KF-FEM The tidal current at the Onjuku coast have been analyzed. KF-FEM is able to estimate a large-scale domain. KF-FEM has been presented. Second MIT Conference on Computational Fluid and Solid Mechanics

21. 1. if goto 6 then else goto 2 2. 3. 4. 5. Off-line 6. 7. On-line Algorithm

22. Result Onjuku Coast Iwawada Port No.5 No.4 No.3 No.2 No.1 Onjuku Port ObservationEstimation